On \(H\)-closed topological semigroups and semilattices

Abstract

In this paper, we show that if \(S\) is an \(H\)-closed topological semigroup and \(e\) is an idempotent of \(S\), then \(eSe\) is an \(H\)-closed topological semigroup. We give sufficient conditions on a linearly ordered topological semilattice to be \(H\)-closed. Also we prove that any \(H\)-closed locally compact topological semilattice and any \(H\)-closed topological weakly \(U\)-semilattice contain minimal idempotents. An example of a countably compact topological semilattice whose topological space is \(H\)-closed is constructed.